# Glencoe Postuales and Theorems Chapters 1 - 4

## 37 terms

### Reflexive Property

For every number a, a = a.

### Symmetric Property

For all numbers a & b, if a = b, then b = a.(ex. the segment GH = segment HG)

### Transitive Property

For all numbers a, b & c, if a = b & b = c, then a = c. (A bit like the law of syllogism)

For all numbers a, b, & c, if a = b, then a + c = b + c and a - c = b - c.(ex. 1 ft = 12 inches, 1 ft + 3 inches = 12 in ches+ 3 inches)

### Mult/Division Property

For all numbers a, b, and c, if a = b, then a c = b c, and if c not equal to zero, a ÷ c = b ÷ c.(ex. 1 m = 1000 mm, 1 m 5 = 1000 mm 5, 5 m = 5000 mm)

### Substitution Property

For all numbers a & b, if a = b, then a may be replaced by b in any equation or expression.

### Distributive Property

For all numbers a, b, & c, a(b + c) = ab + ac.

### THEOREM 2-1 Segment Properties

Congruence of segments is reflexive, symmetric, and transitive.

### Theorem 2-2 Supplement Theorem

If two angles form a linear pair,then they are supplementary angles.

### Theorem 2-3 Angle Properties

Congruence of angles is reflexive, symmetric, and transitive.

### Theorem 2-4 supplementary congruent

Angles supplementary to the same angle or to congruent angles are congruent.

### Theorem 2-5complementary congruent

Angles complementary to the same angle or to congruent angles are congruent.

### Theorem 2-6 right congruent

All right angles are congruent.

### Theorem 2-7 vertical angles

Vertical angles are congruent.

### Theorem 2-8 perpendicular lines form

Perpendicular lines intersect to form four right angles..

### Postulate 3-1 Corresponding Angles

If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.,

### Theorem 3-1 Alternate Interior

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent,

### Theorem 3-2 Consecutive Interior Angle

If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary

### Theorem 3-3 Alternate Exterior Angle

If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent,

### Theorem 3-4 Perpendicular Transversal

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.,

### Postulate 3-5 Euclidean Parallel Postulate

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

### Theorem 3-5 transversal alt int angles

If there is a line and a point not on the line, then there exists exactly one line though the point that is parallel to the given line.,

### Theorem 3-5 transversal alt int angles

If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel.,

### Theorem 3-6

If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.,

### Theorem 3-8

In a plane, if two lines are perpendicular to the same line, then they are parallel.,

### Theorem 3-7

If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel.

### Postulate 3-2

Two nonvertical lines have the same slope if and only if they are parallel.,

### Postulate 3-3

Two nonvertical lines are perpendicular if and only if the product of their slopes is -1.,

### Postulate 3-4

If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.,

### Theorem 4-2 Third Angle Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.,

### Theorem 4-1 Angle Sum Theorem

The sum of the measures of the angles of a triangle is 180.,

### Theorem 4-3 Exterior Angle Theorem

The measure of an exterior angle of a trianlge is equal to,

### Corollary 4-1

The acute angles of a right triangle are complementary.,

### Postulate 4-1 SSS

(Side - Side - Side) - If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.,

### Postulate 4-2 SAS

Side - Included Angle - Side) - If two sides and the INCLUDED angle of one triangle are congruent to two sides and the INCLUDED angle of another triangle, then the triangles are congruent.,

### Postulate 4-3 ASA

(Angle - Included Side - Angle) - If two angles and the INCLUDED side of one triangle are congruent to two angles and the INCLUDED side of another triangle, then the triangles are congruent.

### Postulate 4-3 AAS

(Angle - Angle - Side) - If two angles and a NON-INCLUDED side of one triangle are congruent to the corresponding two angles and side of a second triangle, the two triangles are congruent.